MPs, including some in May’s own party, have expressed anxiety about Trump’s stance on a range of issues, including protectionism and torture. Global trade experts have warned that Britain may gain little from a bilateral trade deal with Washington.

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But the prime minister will deliver a warm message about the two countries working closely together when she addresses senior Republicans at the party’s annual retreat in Philadelphia on Thursday, before she meets Trump in the White House for face-to-face talks on Friday.

May will tell Republicans: “The United Kingdom is by instinct and history a great, global nation that recognises its responsibilities to the world. And as we end our membership of the European Union – as the British people voted with determination and quiet resolve to do last year – we have the opportunity to reassert our belief in a confident, sovereign and global Britain, ready to build relationships with old friends and new allies alike.

“So as we rediscover our confidence together – as you renew your nation just as we renew ours – we have the opportunity, indeed the responsibility, to renew the special relationship for this new age. We have the opportunity to lead, together, again.”

May’s arrival comes as Trump signs off a volley of executive orders in a very public show of swiftly undoing the work of the Obama administration and beginning to honour pledges made on the campaign trail.

On Wednesday, Trump signed two executive orders to boost border security and crack down on immigrants living in the US illegally. On Tuesday, he angered Native Americans and climate change activists by signing executive orders to allow construction of the Dakota Access and Keystone XL oil pipelines. And on Monday, he reinstated the “global gag rule”, which bans aid funding for groups that offer abortions or abortion advocacy even if they use their own funds to do so.

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Downing Street knows that many British voters are sceptical about Trump and his populist policies, some of which he has already taken steps to put into action. Thousands of people joined Women’s Marches in cities across Britain last weekend to protest against his stance on women’s rights.

But May has judged there is more to be gained by striking up what Downing Street sources called a “grown up” relationship with the new president than by remaining aloof.

Jeremy Corbyn, the Labour leader, accused the prime minister of “threatening European partners while offering a blank cheque to President Trump”, while the SNP’s Angus Robertson pressed her on whether she was willing to downgrade Britain’s food standards to win a trade deal.

Andrew Tyrie, a senior Tory MP, also underlined the degree of concern in May’s party about Trump. At prime minister’s questions, he said: “President Trump has repeatedly said he will bring back torture as an instrument of policy. When she sees him on Friday, will the prime minister make it clear that in no circumstances will she permit Britain to be dragged into facilitating that torture, as we were after 11 September?”

Jeremy Corbyn said May was offering a blank cheque to Trump. Photograph: PA

A spokeswoman for the prime minister later said: “We don’t condone torture, inhumane or degrading treatment in any form. That is very clearly the UK’s position. There are going to be issues where we differ on approach and view with President Trump. The benefits of a close, effective relationship is we will be able to raise these directly and frankly with the president.”

May also hopes that by establishing a close relationship, she can persuade Trump to stick to his pledge of pursuing a bilateral trade deal with the UK that could be put into effect after Brexit.

But trade experts are sceptical that a deal can be negotiated quickly – and warn that the US may take advantage of its superior bargaining position as a much larger economy to force open Britain’s markets to US firms.

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Adam Posen, a former member of the Bank of England’s monetary policy committee who is now president of the Peterson Institute of International Economics in Washington, said: “It would require an enormous, transformative relationship with the US to make up for the decline in trade with the EU.

“For 70 years, since the second world war, the US, beyond very narrow intelligence-sharing, has always treated the UK as subservient, or wanted it to be subservient.”

He added: “There’s a lot of reasons to think there will be very small upsides; I can say with very great confidence any gains made from such [a deal] will be a small fraction of what they’ll lose.”

Namali Mackay, trade adviser at manufacturers’ group EEF, said while there might be opportunities for British firms from a bilateral deal, average tariffs between the US and the EU were already low, at an average of 2%. She said the most likely blueprint for a future agreement would be the highly controversial TTIP agreement between the US and the EU.

“We’d have to assume that much of the work that’s already gone on for TTIP will form the basis,” she said.

Asked whether she thought a deal could be ready for signing as soon as Britain leaves the EU, Mackay said: “No, I would categorically say no.” She added that it could take five to 10 years.

Peter Mandelson, who negotiated with the US as the EU’s trade commissioner, said any deal was unlikely to bring rapid benefits for the UK. “If the agreement has real content and is not just for optics, the US will drive a hard bargain. They are tough and ultimately it will be the American way or no way, leaving us even more isolated from Europe and what should remain as our biggest export market,” he said.

Government ministers are hopeful of gaining better access to a large market for high quality British cheese in the US. One ministerial source told the Guardian concerns about lower environmental standards for meat and other food production in the US would have to be ironed out during trade negotiations.

The source emphasised the government’s belief that there was big potential for British dairy farmers and cheese-makers to export more. A spokeswoman for the the industry’s lobby group, Dairy UK, said its members had identified the US as a prime target market for dairy exports outside the EU – and that with 19.7% of the UK’s dairy exports to non-EU countries by value, the US is currently the most important non-EU market. However, losing access to the EU single market was a more pressing concern. “Obviously, a trade deal with the US is high on the agenda but the government can’t forget that, with 80% of the volume of UK dairy exports currently going to EU countries, it is also imperative to avoid disruption to current agreements with the EU,” the spokeswoman said.

Theresa May’s timetable

ThursdayMay will fly to Philadelphia where she will give a speech to senior Republicans at the party’s annual retreat. She will also hold meetings with key Republican leaders who will be crucial to delivering Trump’s agenda in Congress. May will then go to Washington.

FridayShe will lay a wreath at the Tomb of the Unknown Soldier in Arlington cemetery, before holding talks in the Oval Office with Trump. The pair are expected to discuss defence and security cooperation, Nato and trade. She will then travel to Ankara, where she is due to hold bilateral meetings with the president, Recep Tayyip Erdoğan, and the prime minister, Binali Yıldırım.

• This article was amended on 26 January 2017 to clarify the views of Dairy UK by adding more of what its spokeswoman said.